The scaling of transformer-based Large Language Models (LLMs) has significantly expanded their context lengths, enabling applications where inputs exceed 100K tokens. Our analysis of a recent Azure LLM inference trace reveals a highly skewed long-tail distribution of input lengths, with approximately 80% of inputs shorter than 2K tokens. Long inputs constitute only a small fraction. Existing cluster-level LLM scheduling strategies, including First-In-First-Out (FIFO), reservation-based, and priority-based approaches, primarily target short-input requests with lengths below 2K and fail to address this heterogeneity, leading to inefficiencies such as head-of-line blocking, resource underutilization, and starvation of long-input requests. We propose PecSched, a Preemptive and Efficient Cluster SCHEDuling system for LLM inference. PecSched introduces the following key techniques: 1) preemptive scheduling that prioritizes short-input requests for their performance; 2) coordinated prefill-decode colocation and disaggregation, which reduces both the duration and frequency of preemptions; 3) fast Sequence Parallelism (SP) that minimizes the prefill time of long-input requests to further reduce the likelihood and frequency of preemptions. Evaluations based on Azure LLM inference trace show that, compared to state-of-the-art cluster-level LLM inference schedulers, PecSched reduces the 99th percentile queueing delay of short-input requests by up to 92% and improves their throughput by up to 595%, without significantly affecting the Job Completion Time (JCT) of long-input requests. We open-sourced our code.